A NONPARAMETRIC VERTICAL MODEL: AN APPLICATION TO DISCRETE TIME COMPETING RISKS DATA WITH MISSING FAILURE CAUSES Bonginkosi D. Ndlovu1 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg, South Africa e-mail: bongi@dut.ac.za Sileshi F. Melesse School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg, South Africa Temesgen Zewotir School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa Discrete time competing risks data continue to arise in social sciences, education etc., where time to failure is usually measured in discrete units. This data may also come with unknown failure causes for some subjects. This occurs against a background of very limited discrete time analysis methods that were developed to handle such data. A number of continuous time missing failure causes models have been proposed over the years. We select one of these continuous time models, the vertical model (Nicolaie et al., 2015), and present it as a nonparametric model that can be applied to discrete time competing risks data with missing failure causes. The proposed model is applied to real data and compared to the MI. It was found that the proposed model compared favorably with the MI method. Key words: Discrete Time Competing Risks, Missing Failure causes, Nonparametric Vertical Model, Relative hazards, Total hazards. 1. Introduction Discrete time competing risks data arise in survival analysis experiments when subjects are exposed to multiple risks of failure and the time to failure evolves discretely. Time to failure ˜ T is measured in discrete units if ˜ T ∈{1,..., q} for some positive integer q. This occurs when ˜ T is inherently discrete or when ˜ T is originally continuous but observed failure times have been grouped into intervals. The distinguishing feature of this data is an excessive number of event/censoring ties. In education, for example, students may exit the system either by graduating or withdrawing. There are often a substantial number of graduation ties because students can only graduate at the end of the year or semester. Even though students can withdraw continuously throughout the year or a semester, and in most instances informally, the authorities are able to ascertain a withdrawal if a student 1 Corresponding author. MSC2010 subject classifications. 62-07, 62G05. South African Statistical Journal Vol. 54, No. 2, 231–241 httpsȷ//doi.org/10.37920/sasj.2020.54.2.7 © 2020 South African Statistical Association 231